Investigation on coal damage and fracture extension law of liquid nitrogen injection pre-cooling and fracturing under true triaxial stress

• A THMD coupling model for LN2 fracturing coal was developed, incorporating coal heterogeneity and nitrogen thermophysical parameters, and validated against experimental data. • During LN2 fracturing, coal permeability and damage increase exponentially while temperature decreases exponentially. • Longer pre-cooling times expand the damage range and enhance fracture propagation, while reducing and stabilizing initiation and rupture pressures. • Higher horizontal stress ratios cause fractures to preferentially extend along the maximum horizontal principal stress direction, significantly lowering initiation and rupture pressures (by up to 48.07% and 41.36%, respectively).